Calculate pressure and temperature (PT) compensation for gas flow: convert actual flow to standard flow from gauge or absolute pressure and temperature.
Related Calculators
- CFM from Differential Pressure Calculator
- CFM Temperature Rise Calculator
- Exhaust Fan Calculator
- Duct Velocity Calculator
- All Construction Calculators
Flow Compensation Formula
For the same gas composition, define r = density(actual) / density(base) = (Pactual / Pbase) * (Tbase / Tactual) * (Zbase / Zactual), using absolute pressures and absolute temperatures. Actual volume to base volume uses Qbase = Qactual * r; the inverse divides by r. This is a full ratio, not a square root. Base pressure and temperature are explicitly chosen; SCFM does not have a universal temperature reference.
A DP meter indicated on a base-density volume scale instead uses Qbase = Qindicated * โ(r), with Qactual = Qindicated / โ(r), under unchanged composition and meter coefficients. This assumes square-root extraction is already applied to the indicated flow. Optional mass flow is Qbase times density at those exact base conditions. See the Emerson Flow Measurement manual and Yokogawa gas compensation note. The following separate restriction formula does not substitute for gas volume conversion.
Fixed-restriction flow scaling
For many common cases of incompressible flow through the same fixed restriction (e.g., an orifice or valve at similar operating conditions), flow varies approximately with the square root of differential pressure. A common compensation relationship is:
Variables:
- Qโ is the compensated (target) flow rate (e.g., L/min)
- Qโ is the known flow rate at the original condition (same flow units as Qโ)
- ฮPโ is the original differential pressure across the restriction (any pressure unit)
- ฮPโ is the target differential pressure across the restriction (same unit as ฮPโ)
- ฯโ and ฯโ are the fluid densities for the original and target conditions (kg/mยณ). If the fluid and temperature are the same, you can set ฯโ/ฯโ = 1.
To calculate the compensated flow, multiply the known flow by the square root of the differential pressure ratio (and, if needed, the density ratio).
What is Flow Compensation?
Flow compensation is the process of adjusting a flow rate to account for changes in operating conditions (most commonly pressure differential and sometimes fluid density). This is particularly important in fluid systems where changes in differential pressure across a restriction can significantly affect the actual flow rate compared to the expected flow rate. A calculation adjusts the reported estimate; it does not control the system or by itself establish meter accuracy. The model must match the meter signal and physical conditions.
How to Calculate Compensated Flow?
The following steps outline how to calculate the Compensated Flow.
- First, determine the known flow rate (Qโ) in liters per minute (or another flow unit).
- Next, determine the original differential pressure (ฮPโ) across the restriction.
- Next, determine the target differential pressure (ฮPโ) you want to compensate to (same pressure unit as ฮPโ).
- If the fluid density changes between conditions, determine densities ฯโ and ฯโ (otherwise assume ฯโ/ฯโ = 1).
- Finally, calculate the compensated flow (Qโ) using the formula above and check your answer with the calculator above.
Example Problem :
Use the following variables as an example problem to test your knowledge.
known flow (Qโ) = 50 L/min
original differential pressure (ฮPโ) = 2 bar
target differential pressure (ฮPโ) = 3 bar
With unchanged density and restriction coefficient, Q2 = 50 * โ(3/2) = 61.237244 L/min. Select Fixed-restriction flow for this example. The simplified relationship does not model cavitation, compressible choking or changes in flow coefficient.
